Lab Session 13

## 
##  Ljung-Box test
## 
## data:  Residuals from STL +  ETS(M,N,N)
## Q* = 16.351, df = 6, p-value = 0.01199
## 
## Model df: 2.   Total lags used: 8

Lab Session 14

Now try it on the training/test split

##                      ME      RMSE       MAE        MPE     MAPE      MASE
## Training set -0.2181675  8.577369  5.334122 -0.1992749 3.014946 0.2758386
## Test set      6.4831057 15.621518 11.655136  2.7094655 5.170648 0.6027114
##                      ACF1 Theil's U
## Training set -0.007305493        NA
## Test set      0.725258345  0.660509

Lab Session 17

## Series: train 
## ARIMA(1,1,0)(1,1,0)[12] 
## Box Cox transformation: lambda= 0 
## 
## Coefficients:
##           ar1     sar1
##       -0.2172  -0.3909
## s.e.   0.0539   0.0507
## 
## sigma^2 estimated as 0.003085:  log likelihood=488.63
## AIC=-971.26   AICc=-971.19   BIC=-959.85
## Series: train 
## ARIMA(1,1,0)(2,1,2)[12] 
## Box Cox transformation: lambda= 0 
## 
## Coefficients:
##           ar1    sar1     sar2     sma1    sma2
##       -0.2133  0.3171  -0.2293  -1.1526  0.2972
## s.e.   0.0544  0.1806   0.0671   0.1809  0.1623
## 
## sigma^2 estimated as 0.002121:  log likelihood=544.27
## AIC=-1076.55   AICc=-1076.29   BIC=-1053.72

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,1,0)(1,1,0)[12]
## Q* = 111.14, df = 22, p-value = 6.894e-14
## 
## Model df: 2.   Total lags used: 24

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,1,0)(2,1,2)[12]
## Q* = 28.895, df = 19, p-value = 0.06765
## 
## Model df: 5.   Total lags used: 24

## ETS(M,Ad,M) 
## 
## Call:
##  ets(y = train) 
## 
##   Smoothing parameters:
##     alpha = 0.8031 
##     beta  = 0.0049 
##     gamma = 1e-04 
##     phi   = 0.9767 
## 
##   Initial states:
##     l = 63.945 
##     b = 0.2145 
##     s = 0.9895 0.9373 1.0084 1.1736 1.0097 1.0174
##            0.9782 0.9979 0.9931 0.9466 0.9759 0.9725
## 
##   sigma:  0.0457
## 
##      AIC     AICc      BIC 
## 3383.427 3385.526 3452.611
##    SNaive        HW       ETS      STLF ARIMAmod1 ARIMAmod2 
##  23.40458  59.85277  25.43061  25.71131 134.02186  32.85748

## 
##  Ljung-Box test
## 
## data:  Residuals from ARIMA(1,0,0)(2,1,0)[12]
## Q* = 26.616, df = 21, p-value = 0.1839
## 
## Model df: 3.   Total lags used: 24